Answer:
Final answer is B. [tex]y=\frac{3}{2}x+1[/tex]
Step-by-step explanation:
Given equation is [tex]y=-\frac{2}{3}x-4[/tex]
Now we need to find the equation of the line which is perpendicular to the given line [tex]y=-\frac{2}{3}x-4[/tex]. from the given choices.
First let's find slope of the given line [tex]y=-\frac{2}{3}x-4[/tex].
Compare given line with formula [tex]y=mx+b[/tex]
We get [tex]m=-\frac{2}{3}[/tex]
We know that slope of the perpendicular line is given by -1/m
Then slope of perpendicular line is [tex]-\frac{1}{m}=-\frac{1}{\left(-\frac{2}{3}\right)}=\frac{3}{2}[/tex]
so the choice which has slope [tex]m=\frac{3}{2}[/tex] will be the correct choice.
Hence final answer is B. [tex]y=\frac{3}{2}x+1[/tex]
